\section{Backgrounds}
\label{sec:backgrounds}
\begin{figure}
  \centering{\includegraphics[width=2.5in]{fig/dataforecast}}
  \caption{Mobile data traffic expectation by Cisco (2010 - 2015)\cite{cisco_data}}
  \label{fig:forecast}
\end{figure}

Introducing smart phones such as iPhone and android phone have been
boosting up mobile data traffic. According to Cisco's research
data\cite{cisco_data}, the demand of wireless data traffic is
dramatically growing as shown in Fig.~\ref{fig:forecast}. For example,
in 2010, global mobile data traffic grew by 2.6 times due to the
spreading of smart phones and tablets. The report expects that the
traffic demand will reach 6.3 exabytes per month by 2015, which is
26-fold increasing compared to the demand of 2010. Thus, service
providers are facing with the system overloading issue. % To overcome
% this problem, system upgrade or data offloading is now considered as
% the solution.  

Among the wireless traffics, the amount of trasmission in indoor areas
such as home and office is majority. The percentage of time spent
using mobile internet on the move is approximately 35 percent, while
the percentages at home and at work are 40 percent and 25 percent,
respectively. Moreover, the channels between the base station (BS) of
cellular network and the indoor users are not good because of the path
loss through the walls, especially in noise limited cases in which
thermal noise is the limiting factor for indoor macrocell capacity
\cite{CCU10FD}. Indeed, about 40 percent of users experience slow
accessing to mobile internet at their home at least
\cite{FFconsumer}. % Therefore, to serve the indoor users by indoor
% cells rather than outdoor macrocells can improve system throughput
% significantly.

\begin{figure}
  \centering{\includegraphics{fig/spectralefficiency}}
  \caption{Spectral efficiency\cite{FFoffload}}
  \label{fig:spectral}
\end{figure}

However, the increasing of spectrum efficiency of cellular networks is
not sufficient to support the explosion data demand. Even though LTE
with $2 \times 2$ MIMO is exploited, the spectrum efficiency becomes
just two times of HSPA release 6 (HSUPA) as represented in
Fig. \ref{fig:spectral}. Moreover, the speed of enhancement of
spectral efficiency in cellular network technology becomes slower,
because the efficiency almost achieve Shannon capacity which is
theoretical upper bound. And what is worse, the cost for upgrading
system is so expensive that the providers might hesitate to do
upgrading \cite{DHL11PHY}. 

According to \cite{CAG08FNS}, the throughput of wireless cellular
networks have increased about a million-fold since 1957, where the
improvement comes from wider spectrum, reduced cell size, and PHY
improvement. On the increment of the throughput, however, the
contribution of the PHY improvement is only a 5-fold increase, whereas
the enhancements due to wider spectrum and reduced cell size are
25-fold and 1600-hold, respectively. Therefore, the key approach to
improve the throughput of wireless cellular networks is to make the
cell size be more smaller or use more spectrum bandwidth. However,
exploiting wider bandwidth is hard because the spectrum resource is
very expensive. The obstacle for the making smaller cell is also the operational
costs that include costs for deployment, site rental, and energy supply.
Moreover, in order to organize small cell topologies, the study on the
cell planing and management schemes for the smaller cell topology
should be needed, because there have to be a lot of BSs and the BSs
generate interferences each other or users may change their serving bS
so often because of their mobility. 

% Among the wireless traffics, the amount of trasmission in indoor areas
% such as home and office is majority. The percentage of time spent
% using mobile internet on the move is approximately 35 percent, while
% the percentages at home and at work are 40 percent and 25 percent,
% respectively. Moreover, the channels between the base station (BS) of
% cellular network and the indoor users are not good because of the path
% loss through the walls, especially in noise limited cases in which
% thermal noise is the limiting factor for indoor macrocell capacity
% \cite{CCU10FD}. Indeed, about 40 percent of users experience slow
% accessing to mobile internet at their home at least
% \cite{FFconsumer}. Therefore, to serve the indoor users by indoor
% cells rather than outdoor macrocells can improve system throughput
% significantly.

Femtocells is the solution for both problems that the cost problem for
smaller cell and the indoor channel problem. Femtocells, literally,
are operated with very small base station called {\em femto BS} within
indoor areas in general. Since the femto BSs are deployed by users,
the operational costs for the femtocells are paid by the femto owners.
Therefore, although the femtocell topology has very small cell size,
the burden of network organizational expenditure for operators may be
not significant. About indoor coverage problem, since indoor users
could be served by the femto BS with high channel quality, by using
femto BSs, high quality wireless data service can be given to the
indoor users. This is the main reason for the question why the
femtocell is needed for both users and providers. Technically, because
it is hard to organize the femtocell networks by operators cell
planning, the {\em femto BS}s have to be designed to
connect via broadband network called ISP and configure parameters
(e.g. transmission power level ) automatically, which is the main
technical challenge for the femtocell networks. 

Not only network throughput improvement on indoor areas, but also
economical benefit from femtocells is expected. According to the
report \cite{FFconsumer}, a lot of users are suffered from low quality
of indoor wireless data service and they want to churn within 12
months. Especially, high average revenue per user (ARPU) users are
more willing to move, which reduces the revenue of service
providers. However, due to increasing the service quality of indoor
users, the femtocells make existing users stay and attract more users
who subscribe to the service by other service providers. Although the
economical benefits from femtocell networks, the network providers
have to plan the pricing scheme for femto services. Because users are
in a position of authority for femtocell deployment, the providers
should provide incentives to entice the users to deploy femto BSs.


\begin{figure}
  \begin{center}
    \subfigure[Separate]{
      \includegraphics[width=0.6\textwidth]{fig/femtoseparate}
    }
    \subfigure[Shared]{
      \includegraphics[width=0.6\textwidth]{fig/femtoshared}
    }
    \subfigure[Partially shared]{
      \includegraphics[width=0.6\textwidth]{fig/femtopartial}
    }
  \end{center}  \caption{Femtocell types (spectrum)}
   \label{fig:femtospec}
\end{figure}


The deployment scenarios for femtocells are categorized as various
ways\cite{HC09DO}. At first, according to the spectrum sharing between
femtocells and macrocell, there are three type of femtocells :
separated, shared, and partially shared. As shown in
Fig. \ref{fig:femtospec}, separated femtocell networks use different
spectrum range with macrocell, so that they could not interfere each
other. However, since additional bandwidth is needed to support the
femtocell networks, the spectrum efficiency of this deployment option
is not good. On the other hand, although the users who are served from
macrocells could be suffered from the interference generated by
femtocells, due to the spectrum sharing, in case of shared spectrum
scenarios, the networks use spectrum more efficiently than the
separated case. Partially shared is sophisticated spectrum sharing
scheme. Under partially shared policy, femto BSs use a fraction of
spectrum and, to avoid interference to macro users, users who are
nearby femto BSs are allocated to separated spectrum for
communication. But, the users who are far from femtocells could use
the resource which is allocated to femtocells in order to increase
spectrum efficiency. 

\begin{figure}
  \begin{center}
    \subfigure[Open]{
      \includegraphics[width=0.6\textwidth]{fig/femtoopen}
    }
    \subfigure[Closed]{
      \includegraphics[width=0.6\textwidth]{fig/femtoclosed}
    }
  \end{center}
  
  \caption{Femtocell types (openess)}
  \label{fig:femtoopen}
\end{figure}

Openness is another category for femtocells where `closed' or `open'
denotes each type, which represents whether the femto BSs are allowed
to access for all users. The concept of openness is represented in
Fig. \ref{fig:femtoopen}.  A femto BS is called closed when only the
owner of a femto BS or only his family is permitted to use the femto
BS. On the other hand, when any user can be served from the femto BS,
the femto BS is open. In general, closed femto BSs make significant
interference to the nearby macrocell users, since the femto BSs do not
allow the access of non registered users. On the other hand, although
the open femto BSs solve the interference issue, users might not want
to deploy the open femto BSs. It is because the costs generated from
the operation of femto BSs is charged to the owner. Thus, there are
economical issues for openness. Furthermore, in open femto scenarios,
how to select a serving BS is also important problem, since there
could be unwilling handoff from macrocell to femtocell or vice
versa. Moreover, according to the cell selection, the system
throughput could be improved. Users should select a BS to maximize
system throughput.

% In closed femto scenarios, there are two types of interferences which
% come from femto BSs. The signals from femto BSs could bother the
% nearby macrocell users and neighbor femto BSs interfere each
% others. To overcome the interference to the macro users, power control
% schemes could be exploited. Since the closed femto BSs have a small
% number of users in general, femto BSs might spend the majority of time
% with low density traffic. Thus, when we control the power as a
% function of the traffic density, the interference to the macrocell
% users could be reduced. The interference between femto BSs could be
% also mitigated by using distributed power control algorithm. However,
% the distributed manner is hard to implement. Game theoretic approaches
% could be a good solution to make a distributed power control scheme.


\section{Reference System and Research Issues}
\subsection{Reference System}
Due to the indoor traffic offloading, femtocell topology is dealing
with standardizations such as IEEE 802.16, 3GPP, and femto forum.  The
IEEE 802.16m is a target system of this research, but this thesis is
not limited to the standard. The IEEE 802.16m is air interface
standard from the IEEE, which is one of most advanced standard for
cellular networks. In the standard, femtocell is introduced to induce
coverage extension of indoor area. In the IEEE 802.16m, both open and
closed type femto BSs are considered. Furthermore, spectrum sharing
between femtocells and macrocells is defined as three types, shared
spectrum, partially shared spectrum, and separated spectrum. Adaptive
Modulation Coding scheme (AMC) is exploited to enhance system capacity
in the IEEE 802.16. Moreover, OFDM is main difference compared with
traditional cellular systems called 3G.

In this work, we focused on the case that femtocells are deployed in
distributed manner. Under the IEEE 802.16m system, we will verify the
performance of proposed schemes. The scenarios in which the femto BSs
are deployed in the owner's home are the target of this thesis. Thus,
the system can not use any central control messages. Furthermore, the number of
users who are served by a femto BS is not large and it is hard to know
who is the neighbor node under home deployment scenarios.

\subsection{Research Issues}



\begin{figure}
  \begin{center}
      \includegraphics[width=0.6\textwidth]{fig/femtointer}
  \end{center}
  
  \caption{Femtocell interference scenarios (the numbers in each cell
    represent the order of importance)\cite{foruminter}}
\label{fig:femtointer}
\end{figure}

When the spectrum policy is shared spectrum and femto APs are closed,
there are severe interference problems. Because macrocells and
femtocells use the same frequency band, the transmission signal of
each cell is an interference to their neighbor cells. Moreover, under
closed access policy, since users cannot handover to a femtocell even
though they are located on the nearby of the femto AP, they may get
significant throughput loss due to the interference with femtocells.
3GPP group have announced the interference scenarios by their
technical report \cite{3gppinter}. Fig.~\ref{fig:femtointer} presents
a table which shows interference scenarios related with femtocells,
where the number on each cell denotes the order of the
importance\cite{3gppinter,foruminter}. Because the quality of service
for macrocell users have to be guaranteed, the interference related to
macro users has higher priority than the interference between
femtocells. 


% Among the interference scenarios, there are two types of interferences
% which come from the downlink signal of femto BSs. The signals from
% femto BSs could bother the nearby macrocell users and neighbor femto
% BSs interfere each others. To overcome the interference to the macro
% users, power control schemes could be exploited. Since the closed
% femto BSs have a small number of users in general, femto BSs might
% spend the majority of time with low density traffic. Thus, when we
% control the power as a function of the traffic density, the
% interference to the macrocell users could be reduced. The interference
% between femto BSs could be also mitigated by using distributed power
% control algorithm. However, the distributed manner is hard to
% implement. Game theoretic approaches could be a good solution to make
% a distributed power control scheme.

Among the interference scenarios, there are two types of interferences
which come from the downlink signal of femto BSs. The signals from
femto BSs could bother the nearby macrocell users and neighbor femto
BSs interfere each others, which are the target issues of this thesis.
The interference can be mitigated by the
algorithms on the transmission of femto APs such as power control
schemes.  When we design an
interference mitigation algorithm for the downlink of femto APs,
``distributed'' and ``simplicity'' should be meet. Because femtocell
networks are user based deployment topology, the main features of
femtocells are auto-configuration and self-optimization for
plug-and-play deployments. Therefore, in this thesis, all of proposed
schemes are distributed approaches and simple to implement.

% One of most interesting and important issue is power control, which
% indicates how to set its transmission power level in distributed
% manner. Here, we should consider two kinds of interference,
% interference with macrocell and interference with nearby
% femtocells. Since the femtocell is overlaid with a macrocell, the
% signals from the femto BS generate significant interference to nearby
% macrocell users in shared and closed femto scenarios. For example,
% when a friend of the owner of the femto BS visits the owner's house,
% the visitor gets significant interference from the femto BS and he
% even cannot handoff to the femto BS due to the `closed' femto
% policy. Therefore, the transmission power level of each femto BS
% should be restricted to guarantee the service quality of macrocell
% users. However, when the power is too low, the performance gain from
% femto BSs becomes minor. For that reason, femto BSs should find
% adequate power level. Even for `open' femto policy, the transmission
% power level is sensitive issue, which is closely related with
% femtocell coverage. When the femto AP operates with high transmission
% power under `open' femto policy, unwanted handoffs might be occurred
% more times (e.g., when a user walks through street where some femto
% cells exist, the user experiences handoffs to the femtocells and the
% handoffs brings additional control message overheads). Also, low
% transmission power causes indoor coverage issue.

In fact, we can avoid the interference issues with separate carrier or
open femto policy. However, both approaches have obstacles. In order
to adopt the separate for the spectrum allocation method between
femtocells and macrocells, there are loss on the spectral efficiency
of macrocells because they have to partially use the spectrum. In
regard to openness, the users deploying a femto AP in their house may
be hesitate to open because they do not want to give free gift to the
visiting users. Remark that as we mentioned in \ref{sec:backgrounds},
one of the reason to deploy the femtocells is economical benefit,
since the owners of femto APs shoulder the entire cost on the
operation of the femto APs. Therefore, the economical analysis on
femtocell networks may be the most important issue on femtocell networks.


% In
% view of network performance, open policy might be slightly better than
% closed policy because interference problem becomes more serious under
% closed policy . However, since the owner's backhaul connection is
% exploited to serve other users, to implement the 'open' policy,
% approvals of the backhaul provider and the femto owner are
% needed. Thus, how to induce open policy is an problem on femtocell
% research.  Indeed, whether to adopt `open' or `closed' is more
% economical issue than technical one. For example, the service provider
% should determine how much subsidy will be given to users who decide to
% open his femto BS, where the service provider is willing to get more
% revenue by appropriate subsidy. Moreover, for users, subscribing to
% femto service is an economical decision toward more
% utility. Historically, there are not enough researches for network
% economics, although it is important whether a technology has
% economical advantage. Note that TCP is still widely used although ATM
% is more advanced technology.

\section{Areal throughput measure}

Femtocells enhance system performance significantly. There are two
major reasons for that femtocells improve system utility. At first,
because wireless data traffic of macrocells is off-loaded to the
femtocells, the remaining users in macrocell can be served with the
higher throughput than before. In addition, since femtocells can
simultaneously transmit with macrocells, the total sum network
throughput of the system increases. However, how much of improvement
is achieved by means of femtocells is hard to say. Thus, herein, we
will suggest metrics for the system performance.

In \cite{RFF09EE}, areal spectral efficiency is proposed for the
system performance metric, which is the mean of the achievable rates
in a network per unit bandwidth per unit area. However, the area
spectral efficiency is not suitable for our metric. Because the area
spectral efficiency only consider the system with the fixed number of
BSs, the efficiency cannot recognize the system enhancement due to the
increasing of access points from deployments of femto APs. For
example, when every spot has the same SINR and femto BSs are
deployed to have the SINR value in the femtocells, the area spectral
efficiency is not varied when the femto BSs are removed, whereas the
total system throughput is enhanced by frequency reuse. 

Some works, thus, have exploited total system efficiency for the
system metric. The total system efficiency can be defined as the sum
of the areal spectral efficiency for each cells. For example, if there
are 5 cells and the areal spectral efficiencies for the cells have the
same value $E$, the total system efficiency becomes $5 \times E.$
Because the total system efficiency increases as the number of cells
increases, it can measure the system enhancement due to reducing cell
size. However, still, the total system efficiency does not consider
areal fairness. When we compare two scenarios
that the first one is all of the area having the same throughput 5 and
the second scenario is the areal throughput being 10 or 0 with the
same chance, although both scenarios have the same total system
efficiency, the first one may be better than the second one.

In addition, we should consider load balancing. It is obvious that
the case that each cell has similar number of served users is better
than the case that some specific cells have dense and other cells are
sparse. In femtocell cases, in general, the macrocells have much more users
than femtocells have. Thus, the total system efficiency, in which the cell
throughput is just added without considering the number of served
users, may lose the load balancing effects. 

Therefore, herein, we
suggest metrics that consider followings:
\begin{compactenum}[\em 1)]
\item With the same BS deployment, the larger spectral efficiency
  means the better system.
\item When areal spectral efficiencies of two network
  topologies have the same distribution, the larger number of 
  BSs has the larger value.
\item Uniformly providing throughput for all spaces has the largest
  value among all cases having the same average throughput. 
\item If the distribution of users is proportional to the areal
  spectral efficiency of each cell, the system is in the most
  efficient case in view of load balancing.
\end{compactenum}

The proposed metric is a user-centric measure. Because of mobility of
users, they experience variety types of channel environments during
their move. Therefore, the expected value of the utility of the user
can show the network performance well. Moreover, in order to consider
fairness of area, the utility function uses $\alpha$-fairness
functions~\cite{MW00FECC}. The $\alpha$-fairness functions are
objective functions for optimization of which solution is fair and
efficient congestion controller. The metric $U$ for time duration $T$ is defined as
following:
\begin{eqnarray}
  U &=& \sum_i U_i , \\
  U_i &=& \int_T \frac{1}{1-\alpha}x_i^{1-\alpha}p_i(x_i,t)dt,
\end{eqnarray}
where $x_i$ is the throughput of user $i$ at the time $t$ and
$p_i(x_i,t)$ denotes the probability of user $i$ that the throughput
becomes $x_i$ at time $t.$ 
$p_i(x_i,t)$ is determined by the distribution of SINR, the number of
users in the serving cell, and the mobility pattern of the user. 

The interesting range of $\alpha$ is from 0 to 1 in this work. The
range, where $\alpha \ge 1,$ has measurement problems for coverage
hole. Because the measure has negative infinity value when there are
any zero throughput region, which indicates coverage hole, it is hard
to compare networks according to the amount of coverage
hole. Therefore, in this work, the $\alpha$ from 0 to 1 is exploited
to quantify network performance. 


\section{Previous Works and Problem Description}


\subsection{Traffic density based power control}
In section \ref{sec:backgrounds}, we presented
Fig~\ref{fig:femtointer} that shows interference scenarios. Among the
interferences, In this thesis, we focus on scenario 2 and 5 which are
due to signal from femto APs. Because the victim of scenario 2 is the
downlink of the macrocell, we should mitigate the interference so as
to prevent performance degradation due to femtocells. Thus, there are
some previous works dealing with the interference issue by means of
resource management or power control. 



Many works have focused on interference mitigation by using power
control scheme.  In \cite{C07PMC}, the author suggested a power control
algorithm in which femto BSs measure interference level coming in and
determine transmission power level to get target coverage area. Thus,
the transmission powers of femto BSs are adjusted to adequate level
which are not too high and not too low. However, the scheme could be
diverged to maximum power level when there are so many femtocells and
the femtocells interfere each other. With interference limitation, a
self-organized power control scheme was proposed in
\cite{JY08SUPC}. To suppress interferences to macro BSs, femto BSs set
his maximum available transmission power based on the knowledge of
path losses to each macro BSs. However, the information might have
errors and the scheme is sophisticated.


\subsection{Distributed power control consider fairness}
Game theoretic approaches, generally, are exploited to get distributed
algorithms. Since, under a game model, every player tries to maximize
his payoff without considering other players' happiness, it is
represented as a game model that each node maximizes predefined
function every time slot, where the nodes are players and the function
is payoff. Therefore, in femtocell networks, also, there are some papers
using a game model to organize a distributed power control
algorithm. In \cite{CA09PC}, a macro BS and femto BSs in the macro BS
participate a game, where the payoff of the macro BS is maximized when
SINR value is equal to target SINR. Thus, under this game model, the
SINR of the macro BS is always the target SINR. The payoff of femto
BSs is more complex than that of macro BSs, which consists of reward
function to achieve target SINR and penalty function to restrict
interference to other cells. Therefore, under the proposed game model,
users of the macro BS are able to meet target SINR. However, this game
does not consider inter femto interference. Thus, when femtocells
interfere each other, the scheme could be diverged or 
throughput could be degraded due to the interference. 

Although the previous works have proposed distributed power control
schemes to compensate interferences, there are some unsolved
issues. At first, load based power control is not considered, so far,
while, with high probability, a femtocell has small number of users and thus the
amount of traffic generated in the femtocell could be much smaller than
the cell capacity in large portion of time. Thus, when we consider
traffic load to design power control scheme, the system efficiency
could be improved significantly. Furthermore, dropping transmission
power of femtocells when they do not have heavy traffic, could
suppress unwilling handoff from a macrocell to femtocells. Second,
conventional works do not consider fairness at all. Fairness is also
important in view of providers. Since every user subscribes the same
service with paying the same price, the provider should give fair
service to users. 


% Game theoretic approaches have been exploited to get distributed
% algorithm for femtocell networks. When we design distributed
% algorithms with game theory, who is the player and how to set utility
% function for the player determine the Nash Equilibrium (NE) which is
% stable point of the game model. Thus, in order to use a game model to
% make a distributed algorithm, we should carefully design a set of
% players and payoff functions for the users.  For example, in \cite{CA09PC}, a
% game model is sugguested, where players are a macro BS and femto BSs
% in the macro BS. The payoff function of the macro BS is maximized 


% \subsection{Femtocell Selection}
% A critical issue for femtocell networks is to select a serving AP
% among available femto APs.  Due to the fact that users deploy femto
% APs themselves, there might be multiple femto APs available when a
% user searches for a femto AP. So, the user will need to select a
% serving femto AP from the available femto APs. In general cellular
% networks, a user selects a base station on the basis of the received
% signal strength (RSS). However, in the case of femtocell networks, the
% network throughput might not be good if users select a femto AP on the
% basis of the RSS because the network is not efficient when all the
% users select the same AP. Moreover, since femto cells have a few
% number of users, the traffic for a single user might constitute a
% significant portion of the serving AP's traffic load. To avoid these
% the problem, we should consider load-balancing schemes.  So far, few
% studies have been done on the selection of femto APs, although some
% studies addressed cell selection between a macrocell and a femto
% AP\cite{Moon09p755,Moon10p157}.


  
\subsection{Femtocell Economics}

In
view of network performance, open policy might be slightly better than
closed policy because interference problem becomes more serious under
closed policy . However, since the owner's backhaul connection is
exploited to serve other users, to implement the 'open' policy,
approvals of the backhaul provider and the femto owner are
needed. Thus, how to induce open policy is an problem on femtocell
research.  Indeed, whether to adopt `open' or `closed' is more
economical issue than technical one. For example, the service provider
should determine how much subsidy will be given to users who decide to
open his femto BS, where the service provider is willing to get more
revenue by appropriate subsidy. Moreover, for users, subscribing to
femto service is an economical decision toward more
utility. 

Historically, there are not enough researches for network
economics, although it is important whether a technology has
economical advantage. Whether technology is economically attractive or not has an
effect on the research path. For example, although ATM is much more
advanced protocol than TCP/IP, recently, nobody uses ATM thanks to
economical decision. The operation of networks could be analyzed by
economical views. In view of economics, there are three parts, which
are users, providers and networks. Users pay a price determined by
providers and decide a demand for the networks according to QoS of
networks. Providers get revenue from users
and, to maximize their revenue, they invest to upgrade networks or
control prices\cite{DL00PQ}. The QoS of networks depends on the demand
of users, capacity of networks and the characteristic of the
networks\cite{FD00OPC,W09EMCN}.

So far, in many research area in communication fields, economical
studies have been published. The economics among ISPs, contents
provider and users are one of interesting issue for network economics
\cite{HC10PCAN,HCCR09NP,SS06ENP}, where they deal with the following
questions:  how to build pricing schemes, network neutrality issue and
ISP competition issue. Cognitive radio communications also have
economical issues. Between primary services and secondary services,
pricing and spectrum allocation are more economical issue rather than
technical issue\cite{SCG07EF}. Furthermore, incentive for peer to peer
networks and pricing scheme for two-tier\cite{MW06WAP} networks are also economical
problems.

However, to my best knowledge, economical view about femtocell
networks is not enough. Although the economical gain of femtocell
networks is partially given\cite{walrand}, openness has not been studied
yet. How to induce open femto BSs and How much the operators could get
benefits form open femto BSs are important and interesting issues. In
practical, to deploy open femto BSs, the providers should obtain
approval of the owner of the femto BS because the femto BS is in the
owner's house and might use his power line and ISP network which are
already paid by the owner. Thus, whether the femto policy is open or
closed contains economical issue.

\section{Research Objective}

The objective of this research consists of two parts. In the first part,
we will propose algorithms to enhance system performance for femtocell
networks and analyze the performance of the schemes. In this work, two
power control schemes to mitigate interferences are
proposed. In the second part, economical analysis will be given.

Because users who are served from the macro BS
and nearby femtocells could experience significant interference from
the femtocells or unwilling handoffs, one of the interference
mitigation schemes is to compensate interference to the macrocell and
reduce unwilling handoffs without any performance degradation of the
femtocell. Since femtocell has small number of users and low traffic
density, reducing power based on traffic density could be an efficient
interference mitigate scheme. In the proposed scheme, femto APs check
queue length each frame and estimate traffic density.

The other interference mitigation scheme is for reducing inter femto
interference by using a game theoretic approach. The scheme considers
both fairness and power efficiency of femtocells. Since the femtocells
are deployed in distributed manner, it is imposible to use centralized
scheme or message. Thus, game theory is exploited to design totally
distributed algorithm which does not use any external messages. In
this work, it is also shown that the game converge from any initial
point to an unique equilibrium point.

In the second part, the object is verifying economical aspects of
openness. At first, in monopoly, since users subscribe to a service or
not according to the price policy determined by the provider, the
market is modeled as the Stackelberg game. Under this market model,
with some subsidy to open femto BSs, it is shown that both the provider and users could
be happier than without open femto BSs. In order to reflect real
market system as much as possible, we analyze the market for various
type of open scenario. For example, a open femto BS could allow the
access every user or only the users who deploy a femto BS in their
house. Moreover, three type of pricing policies (flat, volume, tiered)
are considered for this model. In duopoly, since the main concern of
mobile providers might be the decision of when they start to offer the
service in reality, we build duopoly market model as a sequential game
where an incumbent decides early and an entrant follows the market. In
this duopoly market, we find important results that imply that the incumbent  
get much more revenue than the entrant due to the positive externality
of open femto BSs.

\section{Chapter Organization}
The remainder of this thesis is organized as follows. In Chapter
\ref{chp:pc1}, a power control scheme reducing interference to the
macrocell is proposed. The scheme controls the transmission power of
femto BSs based on queue length. In this chapter, a finite state
Markov chain model is exploited to analyze the performance of the
proposed scheme. In Chapter \ref{cha:power-control-scheme}, a
distributed power control scheme considering fairness is proposed. In
this chapter, based on game theory, the convergence of the proposed
scheme is shown and the numerical results show the proposed scheme
enhances the system fairness metric. Chapter
\ref{cha:femtocell-economics} is dealing with economics of
femtocells. In this chapter, the economical benefits of open
femtocells are explained. Finally, conclusions and further study items
are discussed in Chapter \ref{cha:conclusion}.

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